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FoV and Magnification - linear taper?

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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: December/06/2009 at 13:51
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I am really leaning towards the Kahles CL 3-9x42 for my next scope.  In comparing FoV specifications on this scope as well as others (not sure how accurate they really are), the Kahles at 3-9 power lists a FoV of 39' - 13.5' at 100 yards.  Is FoV and magnification on a linear taper?
 
Meaning if set at 6 power, would the FoV be half way in between at 26.25' at 100 yards or does it get skewed/varied throughout the power range? Thanks. 
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: December/06/2009 at 18:20
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No, roughly speaking, the FOV at 6X would be half of what it is at 3X and 1.5 times what it is at 9X. However, there is rarely an exact progression from the low to the high end. If you divide 39 in half (39 * 6/3), you get 19.5 and if you multiply 13.5 X 1.5 (13.5 * 9/6) you get 20.25. It might be reasonable to average those two values (19.875) and consider the scope to have about a 20' FOV @ 6X.

If my math is right, a 3-9 scope would typically show half of its FOV (.e.g 26.25) around 4.5X.

Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: December/06/2009 at 19:09
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There is often some field of view constriction at the lowest magnifications.  For example, in a typical 3-9x42 scope there is very little difference in field of view between 3x and 4x, but from 4x onward it changes as you would expect it to.

For the scope in question, at 6x, I would expect the field of view to be just about 1.5 times the field of view at 9x.

ILya
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: December/06/2009 at 20:32
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Originally posted by koshkin koshkin wrote:

There is often some field of view constriction at the lowest magnifications.  For example, in a typical 3-9x42 scope there is very little difference in field of view between 3x and 4x, but from 4x onward it changes as you would expect it to.
 
ILya
 
Really!  Now that is interesting.  Should be easy to check out.
 
Is this the reason why on some models of scopes the 50mm objectives have a larger FOV than the 40 mm objectives, all other things being equal?
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: December/06/2009 at 20:35
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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: December/06/2009 at 20:39
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Originally posted by sakomato sakomato wrote:

Originally posted by koshkin koshkin wrote:

There is often some field of view constriction at the lowest magnifications.  For example, in a typical 3-9x42 scope there is very little difference in field of view between 3x and 4x, but from 4x onward it changes as you would expect it to.
 
ILya
 
Really!  Now that is interesting.  Should be easy to check out.
 
Is this the reason why on some models of scopes the 50mm objectives have a larger FOV than the 40 mm objectives, all other things being equal?

I am not sure how that is related, so please a little further on what you mean.  

Generally speaking, objective lens diameter has zero direct effect on field of view.  There is, however, an indirect effect where with a larger objective lens a scope will often have a little less field of view.

ILya
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: December/06/2009 at 22:57
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Well I went looking for examples and they are hard to find, but I remember looking at these 2 Zeiss Conquests and comparing
 
3x9x40 has a FOV of 34'
3x9x50 has a FOV of 37.5'
 
so I was wondering if the larger objective made it possible for the FOV to be fully implemented and the smaller 40mm objective to cut off part of the FOV.
 
That's what I meant but I could be full of beans.
 
 
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: December/06/2009 at 23:19
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Originally posted by sakomato sakomato wrote:

Well I went looking for examples and they are hard to find, but I remember looking at these 2 Zeiss Conquests and comparing
 
3x9x40 has a FOV of 34'
3x9x50 has a FOV of 37.5'
 
so I was wondering if the larger objective made it possible for the FOV to be fully implemented and the smaller 40mm objective to cut off part of the FOV.
 
That's what I meant but I could be full of beans.
 
 

The objective lens does not cut off the field of view.  The field of view of an objective lens system is determined by its focal length, which in turn is determined by lens shapes (curvature), not by the lens diameter.  On top of that, depending on scope design, the field of view may be limited by one of three different optical systems inside the scope: objective, relay and eyepiece.  

In the case of the two Conquest scopes, these are entirely different designs, hence the field of view differences.  That is one of the reasons you pay a fair bit more for the 3-9x50: it shoves a larger diameter objective lens into a a shorter scope.  It likely has a shorter focal length objective lens system.  It also likely has a wider FOV eyepiece (as evidenced by a considerably shorter eyerelief).

Finally, to convince yourself that objective lens diameter does not effect the field of view, you can do a little experiment.  For example, if you ahve a 3-9x50 Conquest, do this:
-get some optically opaque material (thick black paper for example)
-cut out a circle in the middle of it with an inner diameter of 40mm (or smaller if you wish).
-place it right in front of the objective of the scope aligned with it
-check if the field of view has gotten smaller.

What you will find is the following:
-FOV has not changed
-depth of field has improved
-image sharpness has improved
-image gets a little darker in low light (smaller exit pupil)

ILya
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